Bravais Lattices – The Tetragonal Lattices
There are two tetragonal Bravais lattices. As a tetragonal lattice has a four-fold axis of rotation, there must be a unit cell representing the lattice with \(90^{\circ}\) angles and two axes of equivalent length. Shown below is the primitive and body-centred tetragonal unit cells. As a four-fold rotation axis parallel to the c axis will shift the a axis onto the b axis, these must be the same length for this four-fold rotation axis to be present. The tetragonal lattices have just two lattice parameters free to vary: a and c.
The face-centred and base-centred tetragonal unit cells are equivalent to the unit cells above. Have a go at drawing the lattices in 2D and showing this yourself. The solutions to this can be seen here.